A typical K'NEX construction toy set is furnished with multiple rods of various lengths, based upon a specific system of graduated lengths as described in, for example, the Glickman U.S. Pat. No. 5,350,331, the content of which is incorporated herein by reference. The typical set also includes a variety of generally flat connectors, each provided with a hub and one or a plurality of up to eight rod-receiving sockets disposed at regular angular intervals of 45°. Some connectors are arranged to be joined together at right angles to provide multiple rod-receiving sockets extending in two planes. Because of the basic structure of the connectors, rods joined therewith are for the most part rigidly mounted with respect to other rods. In some cases, the hub of the connector may be supported by a rod for rotational movement, but in such cases the connector may rotate freely about the axis of the rod. While the rotational connector may be fixed in one or more angular orientations in a finished structure, it is not incrementally adjustable. There remains a need for a simple, effective, easily constructed mechanism to enable incremental rotational positioning of assembled rigid components in a K'NEX rod and connector construction set, especially for poseable action figures and the like.